A090332 - OEIS

A090332

Numbers with no divisors >1 that are prefixes of other divisors in binary representation.

1, 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 33, 35, 37, 41, 43, 47, 49, 53, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 121, 125, 127, 129, 131, 133, 137, 139, 141, 143, 145, 149, 151, 155, 157, 161, 163, 167, 169, 173, 179, 181

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OFFSET

1,2

COMMENTS

A090333 is a subsequence.

Complement of A090334.

Divisors >1 of a(n) in binary representation form a prefix code.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

A090330(a(n)) = 0.

A090331(a(n)) = 1.

EXAMPLE

Divisors >1 of a(188)=637: {7,13,49,91,637}, in binary: {111, 1101, 110001, 1011011, 1001111101}.

MAPLE

filter:= proc(n) local d, i, j;

d:= numtheory:-divisors(n);

for i in d do

for j from 1 to ilog2(i)-1 do

if member(floor(i/2^j), d) then return false fi

od od;

true

end proc:

select(filter, [$1..200]); # Robert Israel, Jul 08 2020

MATHEMATICA

filterQ[n_] := Catch@Module[{d = Divisors[n], j}, Do[

For[j = 1, j <= Floor@Log[2, i]-1, j++,

If[MemberQ[d, Floor[i/2^j]], Throw[False]]], {i, d}];

True];

Select[Range[200], filterQ] (* Jean-François Alcover, Dec 15 2021, after Robert Israel *)

CROSSREFS

Cf. A090330, A090331, A090333, A090335, A088862.

Sequence in context: A235868 A319151 A180934 * A325395 A070566 A325623

Adjacent sequences: A090329 A090330 A090331 * A090333 A090334 A090335

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Nov 26 2003

EXTENSIONS

Missing term 121 inserted by Robert Israel, Jul 08 2020

STATUS

approved